Individual Asset Liability Management iALM · Individual Asset Liability Management iALM E A Medova ... SIPP, 401K, individual savings, etc Individual Should individuals rely on social

1

HPCFinance

Aarhus University 23 January 2013

Individual Asset Liability ManagementiALM

E A Medova

Cambridge Systems Associates

© 2013 Cambridge Systems Associates Limited

[email protected] www.cambridge-systems.com

Problems of Aging and Financial Planning

Life-Cycles

Earning years

Retirement

Consumption investment& savings

Pensions:NIDBDC

SIPP, 401K, etc


Dependent years

gdecisions

2

Impact of the Financial, Economic and Fiscal Crisis on Pensions


State pensions Governments Reduced state social security guarantees due to high national debtsLoss in value of institutional pension funds due to current crash in asset prices and low interest rates

DB Corporate

Pensions and Risks

Low asset returns predicted for the next decade with the possibility of high inflationLoss in value of savings due to low saving ratesReduced willingness of corporates/governments to accept funding risk of pensions and the move to 3rd pillar pension plans

DC Corporate and Individual


SIPP, 401K, individual savings, etc

Individual Should individuals rely on social security or take control of their future through individual financial planning?Institutional ALM techniques for financial planning

3

Theoretical Models and Solutions• Theoretical models assume that investors derive

utility from consumption which is supported by financial wealth

A l i l i il bl f f li −Analytic solutions are available for portfolio of riskless and risky assets when the utility function takes some standard form−More complex models include stochastic

labour income, variation in risk aversion across households, liquidity constraints, …Numerical solutions by dynamic


−Numerical solutions by dynamic programming are available for a small number of decision variables and assets due to the computational complexity of problem

Short and Long-term Investors

• Short term investors: the classic mean-variance analysis of Markowitz (1952)

Static analysis which assumes that investors care only −Static analysis which assumes that investors care only about risk and return one period ahead−Financial wealth does not take into account income

• Long-term investors−Special case of myopic investors−Life cycle consumption investment models (Samuelson


e cyc e co su pt o vest e t ode s (Sa ue so 1963, 1969; Merton 1969, 1973; ….)

4

Life Cycle Consumption Investment Models • Benchmark model has many simplifying assumptions on financial and

labour markets and on investor’s preferences[Bovenberg et al, De Economist, 2007]

− availability of risk free asset (bond), only one aggregated risk factor traded h h i h i h i i fl i h l ili f through equity, no housing; the interest rate, inflation, the volatility of

inflation and the equity risk premium are constant over time, the prices are not affected by the decision of individuals, log returns are iid normal , …

− the after-tax wage is constant and riskless with fixed retirement age− individuals aim to maximize lifetime utility which depends on consumption

at each point in time, the weight of future expected utilities decline exponentially at the rate of time preference; preferences feature positive and constant relative risk aversion; risk aversion is measured by the curvature of h l f f l h


the utility function for wealth

• Stochastic control type models with complex solution techniques− Campbell & Viceira’s (2002) book for exposition of the analytical models− The dynamic programming approach (proposed first in Samuelson 1969)

Empirical Results• Empirical results from surveys and behavioural

finance (Kahneman and Tversky, 1979; 1992) show that financial decisions of individuals can not be fully explained by Expected Utility not be fully explained by Expected Utility Theory−People are not uniformly risk averse: they are risk

averse on gains and risk-taking on losses−People overweight small probabilities and

underweight large probabilities−There is a reference point (neutral outcome,

benchmark breakeven point) which defines gains and


benchmark, breakeven point) which defines gains and losses: value functions with an inflection point −Household investment choices depend on family

structure, human capital, wealth base, housing needs, age (see, e.g. Bank of Italy Survey, 2006)

5

Financial Planning• Professional financial planners traditionally resisted the

academic solutions based on theoretical models – Asset allocation puzzle of Canner et al [J. Campbell, 2002]

• Common practice is based on the qualitative assessment of i k i d b fi i l d irisk attitude by financial advisers− Risk attitude is usually related to the investor’s age and determined

using questionnaires− Rule of thumb: equity fraction of one’s portfolio equals 100 – one’s age

• Best practice:− Special purpose funds: Retirement funds, educational funds, etc.− Portfolio is constructed using Markowitz single period portfolio mean


g g p pvariance optimization leading to myopic policies based only on current market data

‘Is Personal Finance a Science?’ P. Samuelson, Keynote Address, 2006

‘The myth of risk attitudes’ Daniel Kahneman JPM Fall 2009

“To understand an individual’s complex attitudes towards risk we must know both the size of the loss that may destabilize them, as well as the

h illi i l f h hi l amount they are willing to put in play for a chance to achieve large gains. Temporary perspectives may be too narrow for the purpose of wealth management.The theories - utility theory and its behavioural alternatives - assume that individuals correctly anticipate their reaction to possible outcomes and incorporate valid emotional prediction into their investment decisions. In fact, people are poor forecasters of their future emotions and future tastes – they need help in this task – and I believe that one of


and future tastes – they need help in this task – and I believe that one of responsibilities of financial advisors should be to provide that help.”

New theory and innovative technology – HP Finance Project

6

New Meta-Model for Individual Financial Planning - iALM

• The iALM system is a decision support tool based on the theory of stochastic optimization

• Principal ideas are brought together from behavioural and classical finance and from decision theory

• It allows interactive re-solve of an instance of the problem to obtain long-term financial plans with different data inputs in order to compare the

f th h i i di id l f


consequences of the changes in individual preferences [Medova et al , 2008]

Cambridge Systems Associates’s iALM

Key Features of iALM• Optimal portfolio decisions correspond to the best

possible desirable consumption subject to existing and future liabilities

• Portfolio risks are managed by− constraining portfolio drawdown in each scenario− imposing limits on portfolio asset holdings in each

scenario

• Interactive use of the system allows to look at the


ypossible outcomes for a number of household’s preferences in order to choose a most suitable financial plan over the long-term horizon

7

Dynamic Stochastic Programming• General idea of dynamic stochastic programming− Incorporate many alternative futures in the form of

simulated scenarios for the discrete-time stochastic data process

1,0 1, 2,0 2, ,0 ,

1,0 1,0

stage1 stage 2 stage

: { : ,..., }{ ,..., , ,..., ,..., ,..., }.

u u T T u

t T

t t t t t t

T

t t t += =

=

ω ωω ω ω ω ω ω14243 14243 14243


−Model future decisions and implement current ones to obtain a forward plan to the problem’s horizon

• When current recommended solution is implemented, then all future solutions across future scenarios will follow with certain probability.

Scenario Tree Schemaleaf nodeleaf node1

st

3d stage2d stage1st stage

root noderoot nodeScenario 8


1 2t = 3 41 2t = 3 4

A multi-period 3-3-2 scenario tree

8

Multi-stage Dynamic Stochastic Programme 2,0 2, ,0 ,01.

2 ,0 ,0 1,01,0 1, 2,0 2, ,0 ,

1,0

1 2 |,..., ,..., ,...,

11 1

min ( ) min ( , ) ... min ( , ) ...

. .

u T Tut tT T

t t t t t tu u T T u

t t t ttTx x

t

f x f f

s tA x b

−

⎧ ⎫⎡ ⎤+ + +⎨ ⎬⎢ ⎥⎣ ⎦⎩ ⎭

=

ω ωω x ω xE E

ωx x x x

,

1,1 1,1 1,1 1,1

0,0 0,121 22 2( ) ( ) ( ) ( ) . .t t t tt tA x A x b a s+ =ω ω ω ω

1,0 1,0 1,0 1,0

1,0 ,1,1 1, 1( ) ... ( ) ( ) ( ) . .T T T T

T u

t t t tTu t Tu Tu t TuA x A x b a s+ + + +

+ + ++ + =ω ω ω ω

M

1,

2,0 2,0 2,0 2,0 2,0 2,0 2, 2,0 ,0 ,0 ,0 ,0 ,0 ,0 , ,0

2,0 ,0

1min ( ) ( ) ( , ( ),..., ( )) ... ( ) ( , ( ),..., ( ))ω ω ω ω ω ω ω ωΩ Ω

⎧ ⎫⎪ ⎪+ + +⎨ ⎬⎪ ⎪⎩ ⎭

∑ ∑u

u T T T T T T T u T

t tT

tt t t t t t t t t t t t t t t tf x p f x x p f x x

s t

Deterministic Equivalent


1,0

1,1 1,0 1,1 1,1 1,1

11 1

21 22

. .

( ) ( ) (ω ω ω

=

+t

t t t t t

s tA x b

A x A x1,1 1,1 1,1

1,0 1,0 1,0 , 1,0 1,0 1,0 1,0

2

1,1 1, 1

) ( )

( ) ... ( ) ( ) ( )

ω ω

ω ω ω ω ω+ + + + + ++ + +

= ∈Ω

+ + = ∈ΩM

T T T u T T T T

t t

Tu t t Tu Tu t t t Tu t t t

b

A x A x b

Solution MethodsScenario history ωt ε Ω is a possible realization of the random vector ωt and corresponds to a node of the scenario tree Deterministic equivalent of the stochastic program (SP) is very large sparse linear programming (LP) problem− coefficients and r.h.s. in the constraints are realization of stochastic

random process.Solution method for linear objective− nested Benders or interior point

• The vector for the stochastic decision process is given by


• Implementable decisions correspond to the root node of the scenario tree

1,0 1, 2,0 2, ,0 ,1,0 ,

stage1 stage 2 stage

: { : ,..., } { ,..., , ,..., ,..., ,..., }.= = =14243 14243 14243u u T T ut T u t t t t t t

T

t t t x x x x x xx x

9

Meta-Model Generation


Overview of individual ALMGather

Individual and Market Data

Econometric and Actuarial

d lli

Market dataPersonal data

Model returns on investment classesLiabilities modelEvents model

Modelling

Scenario TreeSimulation

Optimization Model:

Cash-in flows forecastsCash-out flows forecast

Dynamic optimization model for assets-liabilitiesObj i i i i k d l di

Various C t i t

Events


Model:Tailored

Portfolios, Goal Spending, Cashflow

Balances, etc

Objective: maximize risk managed goal spending Constraints

Visualization of decisions

10

Framing of the Problem

• Broad Framing: overall objective is to provide ‘sustainable spending’ over a household’s lifetime in p gterms of desired consumption on multiple life goals specified by preferences and their priorities

• Narrow Framing: maximization of goal consumption at given times (annually)−Each single goal utility function is defined with


Each single goal utility function is defined with respect to reference points chosen by the household in terms of spending on the goal

Value Function of the Prospect Theory• Recall Value Function of the Prospect Theory


reference point

11

Individual Goal Utility – Narrow Framing• Utility function for an individual goal is given by three reference

points• For each single goal the level of spending y is in the range between

acceptable (s) and desirable (g) and minimum (h) spending subject to p ( ) (g) ( ) p g jexisting and foreseen liabilities. Together with goal priorities these values specify the piecewise linear shape of the utility function for each goal

• The objective is to maximize goal spending with a piecewise linear utilityfunction for the year

g

1

1

αs

αg

u (utility)

g

1

1

αs

αg

u (utility)


s gh

1

αh

y (spending)s gh

1

αh

y (spending)

Overall Objective – Broad Framing • To provide ‘sustainable spending’• Optimization problem objective is to maximize the

expected present value (over all scenarios) of life timeconsumption, i.e. spending on goals

C i f ll “ l i ” di h l

( )

{any alive, }1

,

( )

1where ( )

Here is excess borrowing, is total tax payment and is the inflation index at

T

t tt

xs xs it g t t t

g G t

xst t t

C

C

t

τ τ

τ

π π

=

∈

⎡ ⎤⎢ ⎥⎣ ⎦

= − +

∑

∑

1 u

u u z Iφ

z I φ

E


• Consumption refers to all “elective” spending on chosen goals

( )alive alive, , , , , ,,

\

ˆ∈ ∈

= + +∑ ∑sg

m m

d mt g t g t g t g t g t g tg t

g G g G Gα αC φ F F φ y

12

Net wealthGoal Equity

Goal mortgage Interest charges on interest charges , s

g

mg gg t−φ z r

Goal Equity boxes like this exist for each goal g where g is a mortgaged goal (e.g. home

purchase with mortgage).

Net wealthGoal Equity

Goal mortgage Interest charges on interest charges , s

g

mg gg t−φ z r

Goal Equity boxes like this exist for each goal g where g is a mortgaged goal (e.g. home

purchase with mortgage).

Goal Spending Cash Flow Diagram

Goal Equity

g g

Capital goal assetCash

holding

ggoal loans

consumption downpayment

loan repaym

ents goal purchase

mortgaged goal spending

, sg

dgg t

φ F

, sg

mgg t

φ F

, ,s sg gg t g t

φ y

, sg

gg t−−φ z

( ), ,s sg g

d dgg t g t

−φ y F

C

, ,g t g tφ y

Non-mortgaged goal spending

Changes in goal value

Goal Equity

g g

Capital goal assetCash

holding

ggoal loans

consumption downpayment

loan repaym

ents goal purchase

mortgaged goal spending

, sg

dgg t

φ F

, sg

mgg t

φ F

, ,s sg gg t g t

φ y

, sg

gg t−−φ z

( ), ,s sg g

d dgg t g t

−φ y F

C

, ,g t g tφ y

Non-mortgaged goal spending

Changes in goal value


Non-capital goal spending

If g is a non-capital goal (e.g. education, living expenses)

Capital goal asset

, ,s sg gg t g t

φ yIf g is a capital goal with no mortgage Changes in goal

value

Non-capital goal spending

If g is a non-capital goal (e.g. education, living expenses)

Capital goal asset

, ,s sg gg t g t

φ yIf g is a capital goal with no mortgage Changes in goal

value

Creating Individual Financial Plan

• iALM is a meta-model for optimum resource

allocation over networks of cashflows

• The income from portfolio together with the streams • The income from portfolio together with the streams

of labour and other income provides the best desirable

consumption

• Optimal management of various portfolios


• Two types of portfolio: taxable and savings portfolios such as 401K

(USA) or SIPP and ISA (UK)

• Portfolio allocation sub-problem

13

Wealth Generation• Together with stream of income the solution to the portfolio allocations subproblem

provide optimal projected spending on goals

• Fundamental constraints of portfolio allocation subproblem− Initial holding

P f li l− Portfolio value− Portfolio cashflow− Asset inventory balance− Investment limits, position limits− Portfolio drawdown − etc

• Current (root node) portfolio allocation decisions must be implemented

− Two types of portfolio: taxable and saving portfolios such as 401K (USA) or SIPP


and ISA (UK)

• “What if” scenarios and projected optimal expected dynamic investment policy over a

life-time

Cashflow ConstraintsNet wealth

Portfolio

Margin borrowing

−m+P

Interest charges on margin loans

Transaction costs

( )a∑x( )−m

tx+ txa a a ar r+ − −+∑ ∑x x

( )cash mr+m r

ReturnsGoal

Equity(see below)

Interest on goal loans

Net wealth

Portfolio

Margin borrowing

−m+P

Interest charges on margin loans

Transaction costs

( )a∑x( )−m

tx+ txa a a ar r+ − −+∑ ∑x x

( )cash mr+m r

ReturnsGoal

Equity(see below)

Interest on goal loans

Cash holding

( )+z

Qualified account Income

borrowing

+m

mP−P

q−Pq−zq+P

401q k+PqNR+P

401 401qe k q kρ +P

Liabilities

Taxation

Unauthorized qualified withdrawal penalty

Interest charges on income loans

loan r

epay

ment

C D+I I

qC qD+I I

p o+∑ I I

L

avτ τ+I F

qp qr τP

1 1cash

t t+− −z r

xs xs1(1 )t +z r

new

mar

gin

loan

sm

argi

n lo

an re

paym

ent

quali

fied w

ithdr

awalqualified

contributions

asset purchases

asset sales

Coupons and dividends

Regular income

Employer pension contributions

Qualified coupons and dividends

Interest on bank deposits

excess borrowing at tExcess borrowing repaym

ent

Loans secured

on assets

Interest charges on secured borrowing

(see below)

Goal consumption (non capital)

C

goal

spen

ding

income borrowing

income loan repayment

asset borrowing

asset loan repayment

,I t−z

, 1 1(1 )cash sI t t Ir r−

− −+ +z

, 1 1( )cash sI t t Ir r−

− − +z

Cash holding

( )+z

Qualified account Income

borrowing

+m

mP−P

q−Pq−zq+P

401q k+PqNR+P

401 401qe k q kρ +P

Liabilities

Taxation

Unauthorized qualified withdrawal penalty

Interest charges on income loans

loan r

epay

ment

C D+I I

qC qD+I I

p o+∑ I I

L

avτ τ+I F

qp qr τP

1 1cash

t t+− −z r

xs xs1(1 )t +z r

new

mar

gin

loan

sm

argi

n lo

an re

paym

ent

quali

fied w

ithdr

awalqualified

contributions

asset purchases

asset sales

Coupons and dividends

Regular income

Employer pension contributions

Qualified coupons and dividends

Interest on bank deposits

excess borrowing at tExcess borrowing repaym

ent

Loans secured

on assets

Interest charges on secured borrowing

(see below)

Goal consumption (non capital)

C

goal

spen

ding

income borrowing

income loan repayment

asset borrowing

asset loan repayment

,I t−z

, 1 1(1 )cash sI t t Ir r−

− −+ +z

, 1 1( )cash sI t t Ir r−

− − +z


Excess borrowing

Qualified portfolio

borrowing

qa−∑x

qa+∑x

income loans

Interest charges on excess borrowing

Transaction costs (qualified portfolio)

( )qa∑ x

( )0

tx+ txq qa a a ar r+ − −+∑ ∑x x

xstz 1( )t−

xsz

asset sales

asset purchases

and dividends

Qualified returns

xs xs1t−z r

I−z

Excess borrowing

Qualified portfolio

borrowing

qa−∑x

qa+∑x

income loans

Interest charges on excess borrowing

Transaction costs (qualified portfolio)

( )qa∑ x

( )0

tx+ txq qa a a ar r+ − −+∑ ∑x x

xstz 1( )t−

xsz

asset sales

asset purchases

and dividends

Qualified returns

xs xs1t−z r

I−z

14

Portfolio Variables and ParametersSets:all assets, coupon paying assets, dividend paying assets

Parameters:price of asset a at time treturn on asset a at time t

Variables:

value of holding of asset a at time tvalue of asset a sold at time tvalue of asset a bought at time tcash holding (banked cash) at time treturn on asset a at time t

coupon return on asset a at time tinterest rate on cash deposits at time tspread of interest rate on margin loans over cash ratedividend return on asset a at time ttransaction cost (proportional) of purchase of asset atransaction cost (proportional) of sale of asset alower position limit for asset a (proportion of portfolio)upper position limit for asset a

g ( )quantity of asset a held at time tquantity of asset a sold at time tquantity of asset a bought at time tdecrease in portfolio value at time tincrease in portfolio value at time tportfolio value at time tportfolio losses in excess of maximum acceptable lossincome from coupon payments at time tincome from divident payments at t


pp pturnover limit (as proportion of portfolio value) for each assetturnover limit for intial rebalance parameterminimum acceptable portfolio value (proportional to previous time)

income from divident payments at tmargin borrowing at time trepayment of margin loans at t additional margin borrowing at t

Investment Securities and ModelsInvestment securities

• Domestic and International Equities• Government Bonds• Corporate Bonds• Alternatives

T bill d ll b d

Fundamental financial models Multi-dimensional GBM

G i O i Uhl b k (OU)

, ,ln i t i i i td dt dμ σ= +X W

• T-bills and all bond coupons• Treasury Inflation Protected Securities

(TIPS)− Cash− CPI− Other fixed assets

Geometric Ornstein Uhlenbeck (OU) process

OU process

Or

More complex econometric models

( )t t td dt dα β σ= − +r r W

ln ( ln )t t td dt dα β σ= − +r r W


More complex econometric models

Simulation of stochastic processes for asset returns of selected securities according to the specified scenario tree:

Implemented in StochGenTM Simulator [CSA’s STOCHASTICSTM System]

15

Other Features

• Treatment of real estate purchase with alternative t f ttypes of mortgage

• Treatment of borrowing• Assumptions about income growth• Assumptions about healthcare costs• Insurance


iALM Solutions• iALM provides optimum values for many decision variables –

spending, borrowing, saving, etc -- across time simultaneously for multiple scenarios of random processes representing uncertain markets and life circumstancesmarkets and life circumstances

• Current iALM model includes 20 random processes that vary over the client’s lifetime and around 200 mathematically formulated conditions (constraints) per node

• Average desktop computer solving times are 3-5 minutes (Problem size over 3mln non-zero entries)


An interactive process for analysing retirement and saving alternatives

16

Example, FT July 2 2006



17



18

iALM cash flow assumptions


iALM ‘rule-based’ assumptions


19


Two levels of risk management per scenarioAsset class investment limits Portfolio draw down limits


20

Visual Summary of Profile Goals

Getting an

Portfolio

Cash Flows

Getting an Overview


Wealth


21



22



23



24



25



26

Performance of iALM

• Testing on real profiles of UK and US investors and comparison with recommendations of financial d iadvisors

• Comparison with MVO based methodology• Backtesting performance over 10 years: 1995-2005 for

US model• Behavioural aspects tested using ability to analyse


p g y yrelationship between current wealth, earnings, savings and desirable consumption

2007 2009


27

2007 2009


2007

2009


28

2007


2009


29

2007 2009


Various Household Scenarios and iALM SolutionsProfile:

EntrepreneurAge 55

Sanity Check

Deasirable-Acceptable

Return

Volatility

Living

110,000Priority

8

Retirement

110,000Priority 7

Julie

22,000Priority 10

Todd

17,000Priority

10

U-Bequest1 mln

Priority 3

Cottage

500,000

Bequest

500,000Priority

10

Terminal wealth

One income, 2 dependents, retirement at 62, 6 goals

17.1-13.5%

8.069.98

27,005 65,161 17,000 14,500 187,004 76,222 None 173,512

One income, 2 dependents, retirement at 62, 2 goals

14.7-11.9%

7.899.43

31,228 69,207 None None None None None 148,568

Two incomes, 2 dependents, retirement at 62, 6 goals

14.8-11.5%

8.8512.74

35,559 74,151 17,000 14,500 255,820 195,670 None 219,785


9.6-3.8% 8.70%12.07

69,785 95,244 17,000 14,500 None None None 305,189



10.2-5.2% 8.74%12.36

61,531 87,252 17,000 14,000 None None 426,278 300,827


9.2-3.5% 8.71%11.84

70,412 100,505 None None None None None 274,480

30

Retirement Age Tradeoff for a Specific Consumption Pattern (135k-150k) Throughout Life

70$160,000

$162,000

Better lifestyle by working longer

56

58

6062

64

6668

70

$144,000

$146,000

$148,000

$150,000

$152,000

$154,000

$156,000

$158,000

,Po

st-R

etire

men

t


$100,000 $110,000 $120,000 $130,000 $140,000 $150,000

Pre-Retirement

25%

30%

e Sa

ved

Annual Saving and Retirement Age

5%

10%

15%

20%

Ave

rage

% o

f Pre

-Tax

Inco

m


0%56 58 60 62 64 66 68 70

Retirment Age

31

Technical Summary• Average desktop computer solving times are 2-15 minutes− Pimlott profile: 152sec

• iALM provides optimum values for multiple decision iALM provides optimum values for multiple decision variables− Recommended allocation for current year is robust with respect to the

most unfavourable scenarios

• Probabilities of goals and shape of corresponding distributions are a good indication of uncertainty inherited in the plan

• Many other aspects of financial plans are available e g


Many other aspects of financial plans are available, e.g. cashflow statements, graphs of individual cash flows for liabilities, goal spending, taxes, borrowing through life and so on.

User Benefit Summary• Comprehensive, long-term solution to wealth

management tailored to individual needs: − Free format of specification of life goals and their values− Construction of the utility function based on distinct client needs− Hedging against longevity risks by solving random horizon

optimization problem− Combination of life insurance with retirement saving plan− Consideration of different options for borrowing− Optimum use of tax-shield accounts

• Interacti e process f l i i t t d i


• Interactive process for analysing investment and savings alternatives for long term financial planning

• New paradigm in wealth management with support of HPC Finance

32

iALM References

• Medova et al. (2008). Individual asset-liability management. Quantitative Finance 8.9 547-560g Q

• M A H Dempster & E Medova (2011). Asset-liability management for individual households. British Actuarial Journal, 16 (2), pp.405-464.

• M A H Dempster & E Medova (2011). Planning for retirement: Asset liability management for individuals. In Asset Liability Management 2011 Yearbook, G Mitra


y g ,and K Schwaiger, eds., Palgrave Macmillan, London, pp.409-432.

Documents

Individual Asset Liability Management iALM · Individual Asset Liability Management iALM E A Medova ... SIPP, 401K, individual savings, etc Individual Should individuals rely on social